Which lattice type corresponds to a = 2R?

• A. Simple Cubic
• B. Body-Centered Cubic
• C. Face-Centered Cubic
• D. Hexagonal Close-Packed

Answer: (A)

In a crystal lattice, the lattice parameter a is tied to how atoms touch along the directions of the lattice. For a simple cubic arrangement, the nearest neighbors sit along the cube edges, so the center-to-center distance between touching atoms equals the edge length a. If the spheres just touch, that distance must be 2R, giving a = 2R. This matches the given relation. In other structures, atoms touch along different directions, leading to different a-to-R relations (for example, along the body diagonal in a BCC lattice you get a = 4R/√3, and along the face diagonal in an FCC lattice you get a = 2√2 R). Therefore, the lattice type corresponding to a = 2R is simple cubic.